Brannstrom, Niklas, de Simone, Emiliano and Gelfreich, Vassili (2010) Geometric shadowing in slow-fast Hamiltonian systems. Nonlinearity, Vol.23 (No.5). pp. 1169-1184. doi:10.1088/0951-7715/23/5/008

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Abstract

We study a class of slow-fast Hamiltonian systems with any finite number of degrees of freedom, but with at least one slow one and two fast ones. At epsilon = 0 the slow dynamics is frozen. We assume that the frozen system (i.e. the unperturbed fast dynamics) has families of hyperbolic periodic orbits with transversal heteroclinics.

For each periodic orbit we define an action J. This action may be viewed as an action Hamiltonian (in the slow variables). It has been shown in Brannstrom and Gelfreich (2008 Physica D 237 2913-21) that there are orbits of the full dynamics which shadow any finite combination of forward orbits of J for a time t = O(epsilon(-1)).

We introduce an assumption on the actions of periodic orbits which enables us to shadow any continuous curve (of arbitrary length) in the slow phase space for any time. The slow dynamics shadows the curve as a purely geometrical object, thus the time on the slow dynamics has to be reparametrized.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics Q Science > QC Physics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
Journal or Publication Title:	Nonlinearity
Publisher:	Institute of Physics Publishing Ltd.
ISSN:	0951-7715
Official Date:	May 2010
Dates:	Date Event May 2010 UNSPECIFIED
Volume:	Vol.23
Number:	No.5
Number of Pages:	16
Page Range:	pp. 1169-1184
DOI:	10.1088/0951-7715/23/5/008
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Funder:	Academy of Finland, EU

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